Inverse Dynamics
he ultimate aim of biomechanical analysis is to know what the muscles are doing: the timing of their contractions, the amount of force generated (or moment of force about a joint), and the power of the contraction - whether it is concentric or eccentric. These quantities can be derived from the kinematics using the laws of physics, specifically the Newton-Euler equations: Newton (linear): F = m.a (Force = mass x linear acceleration) Euler (angular): M = I(Alpha) (Moment = mass moment of inertia x angular acceleration) These equations describe the behaviour of a mathematical model of the limb called a link-segment model, and the process used to derive the joint moments at each joint is known as inverse dynamics, so-called because we work back from the kinematics to derive the kinetics responsible for the motion (fig. 1). This is easily done when the motion is open-chain, with no resistance to motion at the terminal segment, since all the kinematic variables are known from motion analysis (in this case Rxd and Ryd of the first segment in the chain, the foot, are both zero). When there is contact of the limb with another object, such as the ground, or a cycle pedal, the forces between the limb and the obstructing object in this closed-chain must be measured. This is usually arranged by the technique of strain-gauging, such as used in a force platform used to measure the ground reaction force during walking and running. Such a model is based on several assumptions, e.g.: that the joints are frictionless pin-joints that the segments are rigid with mass concentrated at their centres of mass that there is no co-contraction of agonist and antagonist muscles that air friction is minimal